On the misunderstanding of logic

Maverick claims a great misunderstanding in my earlier post about the usefulness of logic. I don't think so. Maverick's original post, as I understand it, was an objection to the principle of addressing the small questions of philosophy because the 'big questions' are just too difficult, and probably without resolution. His objection is that the small questions are also "widely and vigorously contested", and so this supposed advantage of pulling in our horns is lost, "and we may as well concentrate on the questions that really matter, which are most assuredly not questions of logic and language"

My reply was twofold. First, the 'little problems' are assuredly not without resolution, at least not if Ockham is right. Now Bill's point may not be that there is no uncontroversial resolution of the little problems. I.e. he is not claiming that they are insoluble, but rather that there is no widespread agreement or consensus on how to resolve them. I reply, Ockham's point is about the understanding of logic. There may be disagreement about his resolution, but that is because those who disagree fail to understand logic.

Second, Ockham's point is that the little problems and the big ones are connected. Resolution of the simple, logical problems opens a door to the larger problems (for example, the problem of the Holy Trinity).

… the gateway to wisdom is open to no one not educated in logic. [...] For it resolves all doubts, dissolves and penetrates all the difficulties of Scripture

This addresses Bill's point that the big questions "are assuredly not questions of logic and language". Ockham says that they are, or rather, that the big questions can be resolved by addressing questions of logic and language.

Whether Ockham is right about the understanding of logic is of course widely and vigorously disputed. See, e.g. "The Failure of Ockham's Nominalism".  But that is beside the point. The fact that the both the big and the little questions are widely disputed is not in itself a good reason to go for the big questions.  If you truly believe that the little questions can be resolved and, even better, are a doorway to understanding and resolving the big ones, then that is a good reason to take the little ones first.  The existence of popular disputes, misunderstandings and confusion is not in itself a good reason not to tackle their root cause.

On the great usefulness of logic

The Maverick fires off a broadside today against the usefulness of logic.

If by 'pulling in our horns' and confining ourselves to problems of language and logic we were able to attain sure and incontrovertible results, then there might well be justification for setting metaphysics aside and working on problems amenable to solution. But if it turns out that logical, linguistic, phenomenological, epistemological and all other such preliminary inquiries arrive at results that are also widely and vigorously contested, then the advantage of 'pulling in our horns' is lost and we may as well concentrate on the questions that really matter, which are most assuredly not questions of logic and language — fascinating as these may be.

Against, I cite the venerable Ockham in his prologue to the Summa , as well as my humbly intended summary of the Summa. As Ockham, following the blessed Augustine, rightly asserts, the study of logic (and semantics) "resolves all doubts, dissolves and penetrates all the difficulties of Scripture, as the distinguished teacher Augustine testifies". "The gateway to wisdom is open to no one not educated in logic". For

It often happens that younger students of theology and other faculties overlay their study with subtleties, before they have much experience in logic, and through this fall into difficulties that are inexplicable to them - difficulties which are nonetheless little or nothing to others - and slip into manifold errors…

So if Maverick has a pipe, as I believe he does, he knows what to put in it.

Intentional being

Maverick has a nice post on intentional being.  He mentions Aquinas, but here is the magnificient Ockham on the very same subject.

Abstract particulars

Anthony asks about abstract particulars here. In reply, I am not sure what an abstract particular is, so I am not entirely sure I can answer the question. I don't think Ockham ever discusses such things, and in any case, beginning with distinctions in reality rather than distinctions in language is foreign to his whole project. When he begins to talk about 'concrete' and 'abstract' in Chapter 5 of Part I of the Summa, he is talking about types of term. He says that ‘concrete’ and ‘abstract’ are names that have a similar beginning verbally, but not similar endings. Thus 'human' and 'humanity', 'just', 'justice', 'wise', 'wisdom'and so on. This is a linguistic distinction, and Ockham's whole argument is that we confuse distinction in language with a distinction in reality. If Socrates is wise, then 'wise' denotes him, but so also does 'wisdom'. 'Wisdom' does not denote any common substance or nature, a singular thing common to all wise things. Rather, like 'wise', it denotes all wise things.

What about the distinction between particulars that exist in space and time (trees, chairs, people) and particulars which do not (triangles, numbers, etc)? Ockham does have something to say about this, but it takes up all of chapters 40-62 of the Summa, in his discussion of Aristotle's categories. So, more later.

I was amused by this post from the Maverick which attempts to classify the various forms of nominalism. I particularly liked the idea of 'mad dog nominalism' – a form of the genre that collapses into linguistic idealism.

I pointed out in the comments box that there is a further ingredient in Ockham's nominalism, namely the thesis that by ignorance of logic we are led astray into certain false and fantastical beliefs. This is not a million miles from Wittgenstein.

[Philosophical problems] are, of course, not empirical problems; they are solved, rather, by looking into the workings of our language, and that in such a way as to make us recognise those workings: in despite of an urge to misunderstand them. The problems are solved, not by giving new information, but by arranging what we have always known. Philosophy is a battle against the bewitchment of our intelligence by means of language. [Philosophical Investigations ~109]

On defining nominalism

"According to Ockham, everything in external reality is singular".  This is not a good way of characterising Ockham's nominalism, for it could equally apply to some of the brands of realism which he criticises and caricatures.  For example, a realist who holds that a universal is a singular thing, inhering in some way in many things, also holds that everything (including universals) is singular. But they would clearly not be a nominalist.

A similar observation applies to the so-called  Ockham's razor.  "Do not multiply entities beyond what is necessary". Sure, but realists agree with that too. The disagreement is over what counts as necessary.  Realists would hold that universals are necessary, of course.

Ockham on induction

I have made a start on book III-3 of Ockham's Summa Logicae by translating some of the chapters on induction. The part 3 of the third part is received little attention from philosophers, and as far as I know has never been translated. The chapters I have looked at come across as terribly weak, unlike the powerful and insightful work of the first two parts.

Ockham says that induction "is a progression from singulars to the universal", which is pretty much the modern understanding of the term. He gives the example "this [man] runs, and that one, and so on, therefore every man runs". What does the 'and so on' mean? If it means 'every other man apart from this one and that one', then the argument amounts to 'Man a and man b and every other man apart from a and b run, therefore every man runs', which is trivial, though admittedly valid. Or does he mean that the 'and so on' is a placeholder for a longer proposition which enumerates every man there is, and so does not include the word 'every', but concludes with the word 'every'? But that would not work, because the enumeration would have to conclude 'and there are no more men'. Mathematical induction, of course, is different from any of these. As I understand it, it is an inference from the properties of the successor of every number, to the properties of all numbers of a particular type (the naturals). Thus the antecedent and the consequent of mathematical induction both contain the word 'every'. I may be wrong, I'm sure my mathematically minded commenters will leap in to correct me if so.

De re and de dicto

Tristan Haze recommended this 1977 paper by Kripke which I am working through. He mentions the de re / de dicto distinction on page 258, and once again I am struck by the way that so much of our terminology and ideas are inherited from medieval Latin philosophy and logic.  I discussed this before with respect to a priori.

The de re / de dicto distinction is mentioned in a passage here from Thomas's Summa Theologiae, which I quote here using the Dominican translation.

Latin

English

Unde et haec propositio, omne scitum a Deo necessarium est esse, consuevit distingui. Quia potest esse de re, vel de dicto. Si intelligatur de re, est divisa et falsa, et est sensus, omnis res quam Deus scit, est necessaria. Vel potest intelligi de dicto, et sic est composita et vera; et est sensus, hoc dictum, scitum a Deo esse, est necessarium.

Hence also this proposition, "Everything known by God must necessarily be," is usually distinguished; for this may refer to the thing, or to the saying. If it refers to the thing, it is divided and false; for the sense is, "Everything which God knows is necessary." If understood of the saying, it is composite and true; for the sense is, "This proposition, 'that which is known by God is' is necessary."

I am not sure about the translation. 'De re' is rendered as 'about the thing', and 'de dicto' as 'about the saying.  Correct-ish, but we have the difficulty of translating a Latin term which is probably being used in a technical sense.   He uses the verb consuevit which means 'is usually' or 'is customarily', which suggests that the terminology was established when he was writing in the 1270s.  It certainly was - the distinction is mentioned at the end of this very technical discussion probably written in Paris around the same time (Aquinas taught in Paris in the 1260s).  Even Abelard, writing in the 12th century, mentions it. A dictum - literally 'what is said' - of a proposition is what is said or asserted by the proposition.  In Latin it is expressed by the accusative-infinitive form, e.g.. Socratem currere which means 'that Socrates runs' or 'Socrates's running'.  A de dicto proposition is thus one which has a dictum as subject.  For example, in Socratem currere est verum (it is true that Socrates is running) the subject is Socratem currere, which is the dictum (or refers to it, medieval texts frequently conflate use and mention), and the predicate is verum.  See Catarina's interesting paper here.

When Thomas talks about the composite and divided sense, he almost certainly means what Ockham is talking about here.  (Not yet available with English translation, however).  Ockham's point throughout the Summa is that the dici de omni pretty much always applies to propositions understood de re, and so Frege's puzzle does not apply in such a sense.  In propositions understood de dicto, there are nearly always problems with substitution.  His ideas about this are mostly in Part III-1 of the Summa, none of which is available in English online, and indeed very little of which is available offline. It is a philosophical scandal that the works of one of England's greatest philosophers are not available in the language of his own country. (For much of his life William would have spoken as well as written in Latin, but the language of ordinary people was a form of middle English similar to the English of Chaucer which would still be intelligible to us modern folks).

Ockham's Fregean moment

I am working on chapter 67 of Ockham's master work, where I find something that reminds me of Frege.  Ockham is talking about 'material supposition'.  This is a mode of supposition where a word stands for itself.  It's rather like when a word is enclosed in quotation marks (which the medievals didn't have), except the whole point of quotation marks is that we create a new word to stand for the unquoted word, and so the word precisely doesn't stand for itself.

Ockham claims that there are situations when a word signifies something that it does not materially supposit for. His example is the sentence "animal is predicated of man", in Latin: animal praedicatur de homine.  Note the word 'homine', which is the ablative case of the word 'homo'.  This is important, for Ockham's sentence is true because 'a man is an animal' is true, which in Latin is homo est animal.  Note the nominative case of 'homo'.  So when we say "animal is predicated of man", we mean that animal is predicated of homo, not homine.  But we can only say that using the word homine, at least in Latin.  (Or perhaps the same is really true in English, except the ablative of the word 'man' is the same as the nominative?)  Thus the quoted homine signifies itself, i.e. homine, but supposits for its nominative homo. (Hope that makes sense).

That seems trivial.  But it seems remarkably close to Frege's famous puzzle about the concept horse.  Frege held that simple propositions like 'Red Rum is a horse' are composed of Object and Concept.  The object is signified by the object word "Red Rum" and is thus Red Rum himself.  The concept is signified by the predicate " - is a horse".  Let's call that the concept Horse.  But now the puzzle.  The sentence "the concept Horse is a concept" is also a simple sentence, where the term "the concept Horse" occurs in subject position.  So it signifies an Object, according to Frege.  And so is not a Concept.   Thus, the concept Horse is not a concept.  Frege admits this is odd.

It must indeed be recognised that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept, whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano.

This seems remarkably similar to Ockham's puzzle about homine, although it would take some work to tease out the underlying basis of it, if any.

A piece of enormously complex polyphony sung over a drone of Aristotelianism and a cantus firmus of revelation

A long title to go with the other one today. Michael Sullivan’s perceptive and entertaining ramble on Ockham and Scotus is well worth looking at.

Ockham and Bradley's regress

I am currently working on chapter 51 of Ockham’s Summa Logicae, and I have spotted something that looks very much like Bradley’s regress. He writes

Nec illud quod subiungitur de materia et forma, subiecto et accidente, toto et partibus, et spiritibus unitis corporibus concludit rem relativam mediam inter illa unita. Eadem enim quaestio remaneret de illa re media: quomodo facit unum cum eo in quo poneretur? Aut enim se ipsa, et eadem ratione standum fuit in primis unibilibus; aut alia unione, et tunc procedetur in infinitum.

I am still working on a translation, but it means something like this. The context is Ockham’s argument against the existence of relation as a distinct category of thing separate from the things that are related. He says that the joining of matter and form, subject and accident, whole and parts etc into one object does not imply the existence of a relation-entity intermediate between the two. For the same question would apply to the relation-entity. How is the relation made one with the thing (such as the unity of matter and from) in which it is posited? Either by itself, and by the same reasoning we should have stopped at the first two things capable of being united (e.g. matter and form alone), or by another union, and then there would be an infinite regress.

But this is Bradley’s regress, or something very similar to it.  Bradley did not invent his regress!

An interesting side note: the Latin phrase eadem ratione standum fuit in primo seems to be a stock phrase always used in the context of regress proofs. Burley uses the same argument, and the same phrase here, arguing that if something X exists, this is either because of its essence, or from something added to its essence. If because of its essence, then existence is part of essence. If because of something else Y added to the essence, then Y exists either because of its essence, or by something added to its essence. If by something Z added to Y, then we have to ask the same thing about Z, and so on ad infinitum. But if by its essence, then by the same reasoning we should have stopped in the first place (eadem ratione fuit standum in primo). I.e. if it is enough for Y to exist because of its essence, the same reasoning applies to the starting point X, and we should have stopped there.

A similar argument, and the same phrase, is used by Thomas in lecture 3 on Book 10 of the Metaphysics. When a man is said to be one, the term one does not express a different nature from man, just as being does not express a different nature from the ten categories; for, if it did express a different nature, an infinite regress would necessarily result, since that nature too would be said to be one and a being. And if being were to express a nature different from these things, an infinite regress would also follow; but if not, then by the same reasoning we should have stopped at the first instance (pari ratione standum fuit in primo). See also Summa I Q6 a3 arg3, where he argues that good is good essentially, and not by something added to it, Summa I Q27 a3 arg1, where he argues that no other procession exists in God besides that of the Word, Summa IIa Q109 a6 arg3, arguing that a man does not need grace in order to prepare for grace, and De Potentia Q3 arg 7 arg7, arguing that the forces of nature suffice for the action of nature without God operating therein.

See also Albertus, Metaphysics IV iv (scanned but not corrected or translated), where he argues that there is no medium between odd and even.

It’s interesting because the stock phrase suggests a stock argument, and therefore its use by writers prior to Ockham suggests the argument did not originate with him. But it is a stock argument against multiplying entities. We must choose reason 1 which tells us not to multiply entities, and reason 2 which tells us we must multiply. If we choose reason 2, we get another entity, but then must choose between reason 1a, which tells us to stop there, and 2b which tells us to continue multiplying. But if we choose 2b, we get an infinite regress. Therefore choose reason 1a. But now the crucial point: reason 1a is the same as reason 1, therefore by the same reason whoy not just stop at 1 - pari ratione standum fuit in primo.

Ockham uses this argument all over the place in the Summa, and it is pretty much the basis of his nominalism. But the examples above suggest that it did not originate with him. His genius lay in seeing its application in metaphysics and logic, in using it as the foundation for his nominalistic program, and in writing the Summa, which is a masterpiece of extended argument, intermixed with polemic and some entertaining ranting and abuse. (More on the ranting and abuse later).

Ockham on the continuum

Newly translated, for the first time on the Internet etc., here is chapter 45 of part I of Ockham's Summa Logicae.  Here, Ockham's applies his nominalism to the age-old question of the continuum.  Is a point something separate and indivisible from the line of which it is a point?  Is number something different from the things which are numbered?

Ockham says no. Aristotle’s intention, according to Ockham, was to deny that there is anything indivisible 'in this world below' (in istis inferioribus).  Continuous quantity is nothing other than a single thing having one part at a distance from another part, and discrete quantity (number) is nothing other than the numbered things themselves. The difference between continuous and discrete quantity is simply that the parts of continuous quantity mutally protude onto one another [ad se protensae mutuo], whereas the parts of discrete quantity (i.e. two men) can be as near or as far as you like, with no 'medium' between them.

... in the case of discrete quantity it does not matter whether or not the items which constitute the discrete quantity are distinct in place and situation or not, or whether there is a medium between them. Hence, for two men to be 'two', it does not matter whether there is a medium between those two men or not. For they are two when there is no medium between them, just as when they are distant from each other by a hundred leagues, nor does the predication 'two' of those men vary because of anything to do with nearness or distance. On the contrary, if they were in the same place at the same time they would be two, just as if they were not in the same place.

 The translation is new, and has not been through any of the review stages required in the Logic Museum, so all suggestions welcome.

The Maverick gives an interesting symmetry argument that Ockham’s maxim about not multiplying entities according to the multiplicity of terms does not support classic nominalism, namely the view that there is no singular entity, no 'universal', signified by a common term. He writes

If the Razor forbids the multiplication of categories of entity according to the multiplicity of categories of terms, then I agree, but fail to see how this supports nominalism. There are singular terms and there are general terms. Someone who maintains that only general terms, but no singular terms, enjoy extralingusitic reference would be well within the stricture laid down by the Razor as your formulate it.

I don't disagree. Clearly more is required, and we have to look to Ockham’s semantics to get classic nominalism. Ockham, in common with most 13th and 14th century philosophers of language, held that there is a relation of ‘supposition’ between terms and extra-mental objects. Thus ‘man’ supposits for Socrates, Plato, Aristotle and so on. Exactly the same relation holds between singular terms like ‘Socrates’ and the object they supposit for (in this case, Socrates). The only difference between common and singular term is that the latter are naturally suited to supposit for only one individual, whereas the former can supposit for as many as you like.

Given this, and given the Razor, classical nominalism certainly does follow. It is fruitless to posit a singular entity designated by the common term ‘man’, which Socrates, Plato, Aristotle etc., fall under in some odd way, when you can explain it in the simpler way above. A common term does not signify a singular entity. Rather, it signifies many entities.

In summary, Ockham's maxim does not on its own support classic nominalism.  We have to add his semantics as well.

On not multipying entities

There is a nice post today by the Maverick on “The Use and Abuse of Occam's Razor: On Multiplying Entities Beyond Necessity” There are few points to raise. Maverick writes “Occam's Razor is standardly taken to be a principle of theoretical economy or parsimony that states: Do not multiply entities beyond necessity.” True, it is standardly taken thus, but as Thorburn showed nearly 100 years ago, Ockham did not say exactly that. He actually said that plurality is not to be posited without necessity (Pluralitas non est ponenda sine necessitate). Moreover, it is not ‘his’ razor. Scotus (on the lines of whose thinking Ockham’s thinking is largely developed) used it, and it is probably earlier than that. He also says that is vain to bring about through more what can be brought about by fewer (frustra fit per plura quod potest fieri per pauciora).

Furthermore, the maxim does not really capture the spirit of Ockham’s nominalism, which is better expressed by his claim that one cause of error is ‘to multiply entities according to the multiplicity of terms, and that every term has a (corresponding) real essence’ (Secunda radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei).

He says this at the end of chapter 51 of the monumental and magnificient Summa Logicae, of whose structure you can get a flavour here. Chapters 40-62 are a long discussion of Aristotle’s categories, and Ockham’s objective, after some essential preliminaries set out in chapters 1-17, is to show that most of the ten categories are not really types of being at all, but really types of term. For example, chapter 51 is part of chapters 49-54 on Aristotle’s category of relation (ad aliquid, relatio). Ockham wants to show that the term ‘relation’ is not a name for a particular type of thing, outside the mind, really distinct from some absolute thing (res extra animam, distincta realiter a re absoluta). Otherwise, whenever a donkey moved down on earth below, every heavenly body would be changed in itself, because of the change in its spatial relation with the donkey. Or we might mistakenly suppose that a father is a father by some extramental thing such as ‘paternity’.

We are led into these errors from the ease with which Latin (and other romance languages, but Ockham rarely talks about these) is able to construct abstract terms like ‘fatherhood’ from concrete terms like ‘father’. He discusses this in chapter 5 and subsequently. Such terms have a similar beginning verbally, but different endings, and the abstract nearly always has more syllables than the concrete. Ockham argues that the concrete and the abstract are really synonyms. To say that Socrates has humanity is no more than to say that Socrates is a man. For this reason there are no abstract names corresponding to many concrete names. E.g. though we frequently use the names ‘cow’, ‘donkey’, ‘goat’, there are no corresponding abstract terms like ‘cowhood’ or ‘donkeyness’. And the ancient philosophers did not use this diversity “except as an ornament of speech, or for some other accidental reason, just as in the case of synonymous names.” [--]

Ockham sets: preliminaries

Judging by the comments from 'Belette', we need some preliminary remarks about Ockham sets. Let's begin with plural reference. In English (and Latin, and probably most natural languages) we have plural terms as well as singular terms. We can form plurals either by concatenating singular terms together, as in 'Peter and Paul'. Or we can use an ordinary plural referring term, as in 'those [two] apostles'. Both of these take verbs in the plural form. Thus "Peter and Paul are apostles", "those apostles are preachers". Finally, we can form a collective noun of the form 'an X [of] Ys'. Thus 'a dozen apostles', 'a pair of shoes' and so on. These nouns are grammatically singular, and usually take verbs in the singular. Thus "a pair of shoes is in the cupboard", "one dozen eggs is a good thing to buy". (Although intuitions differ. Do we say that a number of people are in the room? Or is in the room? But this is merely grammatical accident, and has no relevance to logic, I think).

It is a fundamental assumption of Ockham set theory that the singular form of the collective noun is a grammatical feature only, not a logical one, and that we can assert identities using all three forms of plural noun. Thus

1. Peter and Paul are these apostles.
2. These apostles are a couple of apostles
3. This couple of apostles is [or are] Peter and Paul.

The equivalent to a mathematical set containing more than one member, say {Peter, Paul}, is the reference of the expression formed by concatenating the two proper names with 'and'. Thus 'Peter and Paul'. The equivalent to a set defined by comprehension, e.g {x: apostle(x)}, would be the reference of the plural referring term '[all] the apostles'.

There is no real equivalent to the singleton set {Peter}, because the comma in set notation corresponds to the 'and' in Ockham notation, and once we remove the 'and' from 'Peter and Paul', we are left with 'Peter'. Thus in Ockham set theory, {Peter} = Peter, if that makes any sense. Remember that the curly brace is set theoretical notation, and has no equivalent in natural language. Ockham set theory is meant to capture our logical intuitions about the behaviour of plural and collective nouns in ordinary language, not some invented language like set theoretical notation with modern predicate logic.

There cannot be an empty set in Ockham. Once we remove the name 'Peter' from the expression " 'Peter' ", we are left with nothing at all. An Ockham set is identical with its members, and it is impossible that something is identical with nothing.

Set membership is signified in Ockham by the relational term 'one of'. This can be defined in terms of the primitive 'and' mentioned above, as follows.

a is one of Xs if (def) for some Ys, Xs = a and Ys

For example, let the Xs be Peter and Paul and John. Then there are clearly Ys, namely Paul and John, such that

Xs = Peter and Ys.

I.e. Peter is one of those three persons, Peter and Paul and John.

Belette also asked for a definition of 'infinity'. Let's try starting with 'finity' first, by the recursive definition.

1. Any one thing is finite in number
2. If any Xs are finite in number, then those Xs and any one y are also finite in number.

Thus Peter is finite in number, hence Peter and Paul are finite in number, hence Peter and Paul and John are finite in number, and so on.

Then I say that there are 'finitely many things' when there exists an oset O such that O is finite in number, and such that every thing is one of O. And finally, there are 'infinitely many things' when it is not the case that there are finitely many things. This could happen in two ways. In the first, as I have defined it in the previous post. If every oset is such that at least one thing is not one of it, there cannot be an oset O such that every thing is one of O, and so our condition for finitude fails. Or there can be an oset such that it is not finite, and no finite oset contains everything, and so our condition for finitude fails again. I shall argue that of these two ways in which there could be infinitely many things, only the first is possible.

Ockham’s solution to the Trinity problem

In the fifth chapter of the third book of his monumental Summa Logicae, Ockham presents an interesting solution to the problem of the Trinity. He says that the following syllogism is not valid:

Every divine essence is the Father
The Son is a divine essence
Therefore, the Son is the Father

Why not? Surely it is valid by the rule of dici de omni that Ockham frequently applies to arguments. According to this rule, a universal proposition denotes that the predicate is truly affirmed or denied of anything of which the subject is predicated. Thus “every divine essence is the Father” denotes that of whatever ‘divine essence’ is predicated, so also ‘the Father’ is predicated. Since the minor premisses states that ‘divine essence’ is predicated of the son, it follows (by this rule) that ‘the Father’ is also predicated of the Son. So the conclusion “the Son is the Father” apparently follows. Why, then, does he now say that it does not follow?

Ockham answers that the proposition “every divine essence is the Father” does not denote that the predicate is truly affirmed or denied of anything of which the subject is predicated. And so the argument above is not governed by dici de omni, and so it does not have to be valid.

We can only know when such an argument holds, or when not, from sacred scripture, or from the determination of the church. If scripture, or the church, states that the premisses of such an argument are true and the conclusion false, we can be sure that the argument is not governed by ordinary logical laws. He notes also that such an argument is always valid in the physical or ‘created’ world. For “in the world of created things it is impossible that something one in number, simple and singular, really be several things, really distinct” (inter creaturas impossibile est quod una res numero, simplex et singularis, sit realiter plures res distinctae realiter).

Logic Museum links

Work so far on the Ockham translation:

Chapter or section	Description
Index	The division of terms
Book I chapters 1-4	The division of terms
Book I chapters 5-9	Concrete and abstract terms
Book I chapter 10	The definition of 'connotative' and 'absolute' terms
Book II chapter 7	Truth conditions of past and future tense propositions
Book II chapters 12 & 14	Negative and non-referring propositions
Book III.2 chapters 4-7	Of the division of propositions required for demonstration

Chapters 11-17, including Ockham's arguments against the reality of universals, to follow one day.

Also there is Book I question I of the Summa on its own. This is part of a test to understand why Google does not index certain pages, together with a modified translation (in case Google is ignoring it because on other sites).

Ockham's arguments against universals

I am reading, and having a stab at translating, chapters 15-17 of Ockham's Summa Logicae.  This is one of a number of places where Ockham argues against the view that a universal is something really existing outside the mind (one of the important others being questions 4-6 of Dist. 2, Book I of his commentary on the Sentences**).  I have copied one of his arguments is below, in the original Latin, with the translations by Loux*** and Boehner****.

Neither of the translations exactly reflects the Latin - perhaps because of the difficulty in making sense of the Latin.

Latin*	Loux	Boehner
Item, sequeretur quod aliquid de essentia Christi esset miserum et damnatum, quia illa natura communis exsistens realiter in Christo et in damnato esset damnata, quia in Iuda. Hoc autem absurdum est.	Again, it follows that something of the essence of Christ would be miserable and damned, since that common nature really existing in Christ would be damned in the damned individual; for surely that essence is also in Judas. But this is absurd.	Furthermore, it follows that something of the essence of Christ would be miserable and damned; since that common nature which really exists in Christ, really exists in Judas also and is damned.Therefore, something is both in Christ and in one who is damned, namely in Judas. That, however, is absurd.

* Opera Philosophica I - Summa Logicae, St. Bonaventure, N.Y. : Editiones Instituti Franciscani Universitatis S. Bonaventurae, 1974. 899 p., eds Boehner, Philotheus, Gál, Gedeon, 1915- Brown, Stephen.
** Opera Theologica II - Scriptum in librum primum sententiarum, Franciscan Institute, 1967-79, pp. 99-224.
*** Loux, Michael J. 1974. Ockham's Theory of Terms: Part I of the Summa Logicae. Notre Dame, Ind.: University of Notre Dame Press.
**** In Ockham: Philosophical Writings, a selection, Philotheus Boehner, Stephen F. Brown, 1990.

Ockham on semantic independence

In chapter 43 of Summa Logicae, on the properties of substances, Ockham gives a curious argument to support the nominalist view that truth and falsity are not real properties of propositions.  He begins with Aristotle's discussion of contraries, and of the puzzle that the very same proposition (i.e. declarative sentence) can admit of both truth and falsity.  The sentence 'you are sitting' is now true, for you are sitting. But then you stand up, and the sentence is false.  But the sentence hasn't changed.  How can it both be true and false?

Ockham argues that the truth and falsity of propositions are not some sort of quality inhering in them.   Otherwise, it would follow that a proposition was truly altered by the fact that a fly was flying.  And certain heresies would also follow - and here comes the curious argument (my translation).

For if the truth and falsity of propositions are qualities of propositions as whiteness and blackness are qualities of bodies, then whenever some truth exists, ‘this truth exists’ will be true, just as whenever some whiteness exists, ‘this whiteness exists’ will be true. And in the same way of any falsity. Then I accept the falsity of the proposition “God newly creates something”, which according to that opinion is a single quality of the proposition, inhering in it, and as a consequence is something other than God.

Then I ask whether that thing can be created by God, or not. If it cannot, then it is something other than God which cannot be created by God, which is against the Evangelist, who says “All things were made by him: and without him was made nothing that was made.” [John 1.3]. But if it can be newly created by God, let it be given. Then “this falsity is newly created by God” will be true, and “this falsity is newly created by God, therefore something is newly created” will follow, and further “therefore it is true that something is newly created by God”, and as a consequence it is not false, and furthermore “therefore this falsity of the proposition does not exist”, and further still “therefore it is not newly created by God”.

Ockham and Brentano-equivalence

I talked about 'Brentano equivalence' a few times, e.g. here. It is the thesis that "some A-B exists" is convertible with "some A is B", and is closely connected with the thesis that existence is not a predicate. Something very similar can be found in Ockham's Summa Logicae, Book III, part 2, chapter 26. Parallel Latin-English below. Note that the similarity is not exact - Brentano also held that 'every A is B' is equivalent to the negative 'no A is not B', or to 'not: something that is A and not-B exists'. Ockham, by contrast, agreed with Aristotle that 'every A is B' is affirmative, and that it implies the particular 'some A is B'.

On the confusion about the 'existential import' of the universal proposition, I have a piece here.

Latin	English
Si autem propositio dubitabilis in qua praedicatur esse exsistere per propositionem de inesse vel de possibili habeat pro subiecto nomen connotativum vel respectivum vel negativum vel unum compositum ex multis nominibus, quandoque potest demonstrari, quandoque non.	Now if there is a dubitable proposition in which existential being is predicated by an assertoric or de possibili proposition, and the proposition has for a subject a connotative, relative, or negative name, or one composed from many names, sometimes it can be demonstrated and sometimes it cannot.
Talis enim propositio semper aequivalet uni propositioni in qua praedicatur passio de subiecto, saltem large sumendo passionem. Sicut ista proposito ‘eclipsis est’ aequivalet isti ‘aliquid eclipsatur’; et ista ‘calefactivum est’ aequivalet isti ‘aliquid est calefactivum’; et ista ‘habens tres angulos aequales duobus rectis’ aequivalet isti ‘aliquid est habens tres angulos aequales duobus rectis’.	For such a proposition is always equivalent to a single proposition in which an affection is predicated of a subject, at least when we take "affection" broadly. Thus the proposition, "An eclipse exists" is equivalent to "Something is eclipsed"; and "A heatable thing exists," is equivalent "Something is heatable"; and "Something having three angles equal to two right angles exists," is equivalent to "Something is a thing having three angles equal to two right angles."